SPHERES AND COMPOSITE FIGURES: VOLUMES, SURFACE AREAS, AND WEIGHTS

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UNIT 30

• SPHERES AND COMPOSITE FIGURES VOLUMES, SURFACE
  AREAS, AND WEIGHTS

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SPHERES

• A sphere is a solid figure bounded by a curved
  surface such that every point on the surface is
  the same distance from a point called the center
• A round ball, such as a baseball or basketball,
  is an example of a sphere
• The surface area of a sphere equals 4?r2 where r
  is the radius
• The volume of a sphere equals 4/3 ?r3 where r is
  the radius

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SPHERE EXAMPLE

• Determine the surface area and volume of a
  basketball that has a 12-cm radius

• SA 4?r2 4?(12 cm)2 1809.56 cm2 Ans

• V 4/3 ?r3 4/3 ?(12 cm)3 7238.23 cm3 Ans

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VOLUMES AND SURFACE AREAS OF COMPOSITE SOLID
FIGURES

• To compute volumes and surface areas of composite
  solid figures, it is necessary to determine the
  volume or surface area of each simple solid
  figure separately. The individual volumes or
  areas are then added or subtracted

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COMPOSITE FIGURE EXAMPLE

• Determine the total surface area of the figure
  below, given that the circle and triangle are
  holes that were cut out

• First determine the area of the rectangle and
  then subtract the areas of the circle and
  triangle

• Area of rectangle 30" ? 45" 1350 in2

• Area of triangle ½(10")(6") 30 in2

• Area of circle ?(2")2 12.57 in2

• Total surface area of composite figure
• 1350 in2 30 in2 12.57 in2
• 1307.43 in2 Ans

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PRACTICE PROBLEMS

• Round all answers to the following problems to
  two decimal places whenever necessary
• 1. Determine the surface area and volume of a
  sphere with a radius of 14 mm.
• 2. A spherical water tank has a diameter of 8
  feet. It is to be repainted, and the total cost
  of the paint job is 0.28 per square foot.
  Compute the total cost of repainting the tank.
• 3. How many gallons of water will the tank in
  problem 2 hold given that 7.5 gallons 1 cubic
  foot?
• 4. Compute the surface area of a ball that has a
  circumference (great circle) of 25 inches.

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PRACTICE PROBLEMS

• 5. Determine the volume of the figure shown
  below

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PROBLEM ANSWER KEY

• 1. SA 2463.01 mm2
• V 11494.04 mm3
• 2. 56.30
• 3. 2010.62 gallons
• 4. 198.95 in2
• 5. 11434.35 cm3